<p>
  Implement RMS Normalization forward pass for 1D input vectors. Given an input tensor of shape [N] where N is the number of elements, compute the normalized output using a scalar scale (<code>gamma</code>) and shift (<code>beta</code>) parameter.
</p>

<p>
  RMS Normalization computes:
  \[
  \begin{align}
  \text{rms} &= \sqrt{\frac{1}{N} \sum_{i=1}^{N} x_i^2 + \epsilon} \\ 
  \hat{x}_i &= \frac{x_i}{\text{rms}} \\
  y_i &= \gamma \hat{x}_i + \beta
  \end{align}
  \]
</p>

<h2>Implementation Requirements</h2>
<ul>
  <li>Use only native features (external libraries are not permitted)</li>
  <li>The <code>solve</code> function signature must remain unchanged</li>
  <li>The final result must be stored in the <code>output</code> tensor</li>
</ul>

<h2>Example 1:</h2>
<pre>
Input:  input = [1.0, 2.0, 3.0, 4.0]  (N=4)
        gamma = 1.0
        beta = 0.0
        eps = 1e-5
Output: output = [0.36514813, 0.73029625, 1.0954444, 1.4605925 ]
</pre>

<h2>Example 2:</h2>
<pre>
Input:  input = [1.0, 2.0, 3.0]  (N=3)
        gamma = 1.0
        beta = 0.0
        eps = 1e-5
Output: output = [0.46290955, 0.9258191, 1.3887286]
</pre>

<h2>Constraints</h2>
<ul>
  <li>1 ≤ <code>N</code> ≤ 100,000</li>
  <li><code>eps</code> = 1e-5</li>
  <li>-100.0 ≤ input values ≤ 100.0</li>
  <li>0.1 ≤ gamma ≤ 10.0</li>
  <li>-10.0 ≤ beta ≤ 10.0</li>
</ul>
